Question : A can do $\frac{1}{4}$th part of a work in 9 days. B can do $\frac{2}{3}$rd part of the same work in 28 days. Working together, in how many days can A and B complete the whole work?
Option 1: $\frac{262}{11}$ days
Option 2: $\frac{252}{13}$ days
Option 3: $\frac{261}{15}$ days
Option 4: $\frac{198}{17}$ days
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Correct Answer: $\frac{252}{13}$ days
Solution :
Given: A can do $\frac{1}{4}$ part of a work in 9 days.
A does the whole work in $9\times 4=36$ days.
So, A's one day's work = $\frac{1}{36}$.
B can do $\frac{2}{3}$ part of the same work in 28 days.
B does the whole work in $28\times \frac{3}{2}=42$ days.
So, B's one day's work = $\frac{1}{42}$.
The number of days required by A and B to complete the whole work together
= $\frac{1}{\frac{1}{36}+\frac{1}{42}}=\frac{1}{\frac{7+6}{252}}=\frac{252}{13}$ days
Hence, the correct answer is $\frac{252}{13}$ days.
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